1. Field of the Invention
The present invention relates to a musical tone synthesizing apparatus which is suitable for electric wind instruments and the like.
2. Prior Art
Conventionally, a method for synthesizing a musical tone by operating the simulation model of the sound generation mechanism of non-electronic musical instrument is well known. Such method is disclosed in Japanese Patent Laid-Open Publication No. 63-40199, for example. Hereinafter, description will be given with respect to the simulation model of the sound generation mechanism of wind instrument and then description will be further given with respect to the musical tone synthesizing apparatus utilizing such simulation model.
FIG. 1 is a sectional view showing diagrammatical construction of the wind instrument such as the clarinet, saxophone, etc. In FIG. 1, 1 designates a resonance tube of the wind instrument and 2 designates a reed. In addition, TH designates a tone hole formed through the resonance tube 1, by which a tone pitch is to be controlled.
When a performer blows his breath 2A into the reed 2, the reed 2 is vibrated by breath pressure PA and elastic character thereof in a direction as shown by 2S. As a result, pressure wave of air (i.e. compression wave of air) is produced in the tube 1 near the reed 2. Such pressure wave of air is transmitted to a terminal portion 1E of the tube 1 as progressive pressure wave F. Then the progressive pressure wave F is reflected at several portions and terminal portion 1E of the tube 1. Thereafter, reflected pressure wave R is returned to the reed 2, so that pressure PR due to the reflected pressure wave R is applied to the reed 2. Therefore, the whole pressure P to be applied to the reed 2 can be calculated by the following formula (1). EQU P=PA-PR (1).
Thus, the reed 2 is subject to the non-linear vibration which depends on the elastic characteristic thereof and whole pressure P. When the resonance state is stablished between the vibration of reed 2 and reciprocating motion of the pressure waves F, R in the resonance tube 1, the musical tone of the wind instrument is to be generated.
In this case, the resonance frequency is changed over by open/close operation of the tone hole TH formed through the tube 1. More specifically, when the open/close operation is carried out on the tone hole TH by the performer's finger, the flow of the compression wave is varied in the vicinity of the tone hole TH so that the substantial columnar length in the tube is varied, whereby the resonance frequency is to be changed over.
FIG. 2 shows the musical tone synthesizing apparatus whose configuration is obtained by simulating the sound generation mechanism of the wind instrument. In FIG. 2, 11 designates a ROM which stores a non-linear function representing the relationship between the whole pressure P and pressure wave of air generated by the reed 2; 12 designates a resonance circuit which simulate the resonance tube 1; 13 designates an adder; and INV designates an inverter. Herein, data VA which corresponding to the breath pressure PA is applied to the adder 13, while output data PR from the resonance circuit 12 is applied to the adder 13 via the inverter INV. Thus, the addition as shown in the foregoing formula (1) is carried out in the adder 13, and the result thereof corresponding to the whole pressure P is applied to the ROM 11 as its address data. Therefore, the ROM 11 outputs data corresponding to the pressure wave of air, which is then applied to the resonance circuit 12.
In the resonance circuit 12, BD.sub.1, BD.sub.2, . . . designate bi-directional transmission circuits each simulating the transmission delay characteristic of the compression wave of air which propagates in the resonance tube 1. In each of the bi-directional transmission circuit BD.sub.1, BD.sub.2, etc., DF.sub.1, DF.sub.2, . . . designate delay circuits for transmitting the progressive wave signal, and DR.sub.1, DR.sub.2, . . . designate delay circuits for transmitting the reflected wave signal. Each of delay circuits DR.sub.1, DR.sub.2, . . . contains some flip-flops of which number is corresponds to the bit number of the transmitted data each driven by the clock having the predetermined period. Further, TRM designates a terminal circuit which simulates the reflection of the compressive wave of air which is reflected at the terminal portion 1E of the resonance tube 1 (see FIG. 1). This terminal circuit TRM consists of a low-pass filter ML and an inverter IV. Herein, the low-pass filter ML simulates the acoustic loss which is occurred due to the reflection of compression wave, while the inverter IV simulates the phase inversion of the compression wave to be reflected. Incidentally, this inverter IV is not required when the terminal portion 1E is closed but required when the terminal portion 1E is opened.
Furthermore, JU.sub.1 designates a junction which simulates the scattering of the compression wave in the vicinity of the tone hole TH. In JU.sub.1, M.sub.1, M.sub.2 designate multipliers; A.sub.1, A.sub.2 designate subtractors; and A.sub.j an adder. The delay circuit DF.sub.1 in the bi-directional transmission circuit BD.sub.1 outputs progressive wave data F.sub.1 to the multiplier M.sub.1 wherein F.sub.1 is multiplied by a coefficient a.sub.1 so that multiplication result a.sub.1 F.sub.1 is sent to the adder A.sub.j. On the other hand, the delay circuit DR.sub.2 in the bi-directional transmission circuit BD.sub.2 outputs reflected wave signal R.sub.2 to the multiplier M.sub.2 wherein R.sub.2 is multiplied by another coefficient a.sub.2 so that multiplication result a.sub.2 R.sub.1 is obtained. Herein the coefficients a.sub.1, a.sub.2 will be described later in detail. The adder A.sub.j adds these two multiplication results together, and then its addition result is supplied to both of the subtractors A.sub.1 , A.sub.2. The subtractor A.sub.1 subtracts F.sub.1 from the addition result of adder A.sub.j to thereby output its subtraction result to the delay circuit DR.sub.1 in the bi-directional transmission circuit BD.sub.1 as reflected wave data R.sub.1. On the other hand, the subtractor A.sub.2 subtracts R.sub.2 from the addition result of A.sub.j to thereby output its subtraction result to delay circuit DF.sub.2 in the bi-directional transmission circuit BD.sub.2 as progressive wave data F.sub.2. Further, other junction circuits which are constructed similar to the junction circuit JU.sub.1 for simulating other tone holes in the tube 1, are inserted between BD.sub.2 and TRM at corresponding positions of the tone holes.
Next, description will be given with respect to the coefficients a1, to be used in the multipliers M1, M2 with respect to the following two cases.
(i) First Case where the tone hole TH is opened:
The following formula (2) represents air pressure Pj at point j which is set in the vicinity of the tone hole TH in the tube 1 shown in FIG. 1. EQU Pj=a.sub.1 off P.sub.1+ +a.sub.2 off P.sub.2+ ( 2).
Herein, P.sub.1+ designates the pressure of the compression wave which enters into the point j from the reed 2, while P.sub.2+ designates another pressure of the compression wave which enters into the point j from the terminal portion 1E. In addition, a.sub.1 off, a.sub.2 off designate ratios of two pressures of compression waves, which can be represented by the following formulae (3), (4) respectively. EQU a.sub.1 off=2.phi..sub.1.sup.2 /(.phi..sub.1.sup.2 +.phi..sub.2.sup.2 +.phi..sub.3.sup.2) (3) EQU a.sub.2 off=2.phi..sub.2.sup.2 /(.phi..sub.1.sup.2 +.phi..sub.2.sup.2 +.phi..sub.3.sup.2) (4).
In the above formulae, .phi..sub.1 designates the diameter of the tube 1 in reed side; .phi..sub.2 designates the diameter of the tube 1 in terminal side; and .phi..sub.3 designates the diameter of the tone hole TH. In FIG. 2, the progressive wave signal F.sub.1 corresponds to the pressure P.sub.1+, while the reflected wave signal R.sub.2 corresponds to the pressure P.sub.2+. In this first case where the tone hole TH is opened, the above-mentioned coefficients a.sub.1 off, a.sub.2 off are used as the foregoing coefficients a.sub.1, a.sub.2 of the multipliers M.sub.1, M.sub.2 respectively. For this reason, the adder Aj can output the operation result of foregoing formula (2), i.e., signal corresponding to the air pressure Pj at the point j in the tube 1.
Meanwhile, the following formulae (5), (6) respectively represent pressure P.sub.1- of the reflected compression wave which flows from the point j toward the reed 2 and pressure P.sub.2- of the progressive compression wave which flows from the point j toward the terminal portion 1E. EQU P.sub.1- =Pj-P.sub.1+ ( 5) EQU P.sub.2- =Pj-P.sub.2+ ( 6).
Thus, these pressures P.sub.1-, P.sub.2- correspond to the outputs of the subtractors A.sub.1, A.sub.2 respectively.
(ii) Second Case where the tone hole TH is closed:
This case is equivalent to the state where the diameter .phi..sub.3 of the tone hole TH is at "0". Therefore, coefficients a.sub.1 on, a.sub.2 on can be obtained by putting ".phi..sub.3 =0" in the foregoing formulae (3), (4) respectively. EQU a.sub.1 on=2.phi..sub.1.sup.2 /(.phi..sub.1.sup.2 +.phi..sub.2.sup.2)(7) EQU a.sub.2 on=2.phi..sub.2.sup.2 /(.phi..sub.1.sup.2 +.phi..sub.2.sup.2)(8).
These coefficients a.sub.1 on, a.sub.2 on are used as the foregoing coefficients a.sub.1, a.sub.2 of the multipliers M.sub.1, M.sub.2.
Thus, the adder Aj can output the signal corresponding to the air pressure Pj at the point j of the tube 1 in accordance with the following formula (9). EQU Pj=a.sub.1 on P.sub.1+ +a.sub.2 on P.sub.2+ ( 9).
Then, the subtractors A.sub.1, A.sub.2 output signals corresponding to the pressures P.sub.1-, P.sub.2-.
As described heretofore, the circuit shown in FIG. 2 can simulate the scattering state of the compression wave in the tube 1 in response to the open/close operation of the tone hole TH.
In the present example of the conventional musical tone synthesizing apparatus, the data VA corresponding to the blowing pressure PA is applied to the ROM 11 via the subtractor 13. The output signal of the ROM 11 is transmitted to the terminal circuit TRM via the bi-directional transmission circuits BD.sub.1, BD.sub.2 and junction circuit JU.sub.1 etc. In the junction circuit JU.sub.1, values of the coefficients a.sub.1, a.sub.2 are changed over in response to the open/close operation of the tone hole TH as described before, and consequently the scattering state in the junction circuit JU.sub.1 is changed over. The progressive wave data reached at the terminal circuit TRM is processed by the low-pass filter ML and inverter IV so that the reflected wave data is obtained.
The reflected wave data is transmitted through the bi-directional circuits BD.sub.n, . . . , BD.sub.2, BD.sub.1 (Where, BD.sub.n, not shown, designates a bi-directional circuit which is most adjacent to the terminal circuit TRM); junctions JU.sub.1, etc. which are inserted between the corresponding bi-directional circuits. Then, the inverter INV inverts sign of the reflected wave data. Thereafter, the reflected wave data is fed back to the adder 13 so that this circuit shown in FIG. 2 is set in a resonance state. In this case, the resonance frequency can be changed over by changing over the coefficients a.sub.1, a.sub.2 used in the junction circuit JU.sub.1 in response to the open/close state of the tone hole TH.
However, the above-mentioned junction circuit requires two multipliers, two subtractors, and one adder for simulating one tone hole. Therefore, there is a problem in that the hardware of conventional apparatus must be enlarged. In contrast, when the above-mentioned operational process is carried out by the software to be executed by the digital signal processor (DSP) and the like, there is a problem in that the amount of software operations must be increased.